Uniformly accurate integrators for Klein-Gordon-Schrödinger systems from the classical to non-relativistic limit regime

01/14/2022

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by   María Cabrera Calvo, et al.

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In this paper we present a novel class of asymptotic consistent exponential-type integrators for Klein-Gordon-Schrödinger systems that capture all regimes from the slowly varying classical regime up to the highly oscillatory non-relativistic limit regime. We achieve convergence of order one and two that is uniform in c without any time step size restrictions. In particular, we establish an explicit relation between gain in negative powers of the potentially large parameter c in the error constant and loss in derivative.